On the semilocal convergence of a three steps Newton-type iterative process under mild convergence conditions
- Hernández-Verón, M.A. 1
- Martínez, E. 2
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1
Universidad de La Rioja
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2
Universidad Politécnica de Valencia
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ISSN: 1017-1398
Ano de publicación: 2015
Volume: 70
Número: 2
Páxinas: 377-392
Tipo: Artigo
beta Ver similares en nube de resultadosOutras publicacións en: Numerical Algorithms
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Resumo
In this paper the semilocal convergence for an alternative to the three steps Newton’s method with frozen derivative is presented. We analyze the generalization of convergence conditions given by w-conditioned non-decreasing functions instead of the first derivative Lipschitz or Holder continuous given by other authors. A nonlinear integral equation of mixed Hammerstein type is considered for illustrating the new theoretical results obtained in this paper, where previous results can not be satisfied.